Thread by @ReformedTrader

1/ Fortune's Formula (William Poundstone)

"Even unlikely events must eventually come to pass. Therefore, anyone who accepts small risks of losing everything eventually _will_ lose everything. The compound return rate is acutely sensitive to fat tails."

amazon.com/Fortunes-Formu…

2/ "Looked at another way, a coin toss is physics. An event is random only when no one cares to predict it.

"Thorp discovered that he was able to guess approximately where the roulette ball would land: The wheel was slightly tilted. This made the ball favor the downhill side."

3/ "Money management is the tricky & all-important issue of how to extract the greatest profit from a favorable opportunity. You can be the world’s greatest poker player, but if you can’t manage your money, you’ll end up broke. Sadly, almost everyone goes broke in the long run."

4/ "Early in this random-walk chart, wealth hits zero (line marked “Bankrupt”). Had this happened in a casino, the gambler would be tapped out. The right part of the chart is therefore irrelevant. He’s out permanently.

"It is possible to go broke even with a positive edge."

5/ "A greedy better might be tempted to bet his entire bankroll on the basis of the inside tips. But tips are not sure things. Sooner or later, a favored horse will lose. The gambler who always stakes his entire bankroll will lose everything the first time a tip is wrong."

6/ "Kelly concluded that a gambler should be interested in compound return, measuring success not in dollars but in percentage gain per race. The best strategy is one that offers the highest compound return consistent with no risk of going broke."

7/ Given zero transaction costs, "apportion your bets among horses according to your estimate of each one’s chance of winning.

"This way, you bet on every horse and will never be completely broke. If you believe War Admiral has a 24% chance to win, put 24% of your capital there.

8/ "In the long run, “bet your beliefs” will earn you the maximum possible compound return—provided that your assessment of the odds is more accurate than the public’s.

"The bets on the horses you think will lose are a valuable insurance policy.

9/ " But “bet your beliefs” is of little use at a real track, as U.S. racetracks skim anywhere from 14-19% of the amount wagered.

"The Kelly formula says to bet edge/odds of your bankroll on each bet."

For a portfolio, Kelly sizing uses Sharpe ratios:

https://twitter.com/ReformedTrader/status/1229277267731214337

10/ "Elwyn Berlekamp, who worked for Kelly at Bell Labs, remembers Kelly saying that gambling and investment differ only by a minus sign. Favorable bets are called “investments.” Unfavorable bets constitute “gambling.” "

11/ "Shannon suggested that Thorp use Kelly’s formula to decide how much to bet on blackjack based on how favorable the deck was. Despite the theoretical protection against ruin, they realized that there are many variables in casino play."

12/ "In a moderately favorable situation, a card-counter might have a 51% chance of winning. The edge is 2%, so the Kelly formula says to bet 2% of the bankroll. (This estimate is not exact because of the features of splitting pairs and doubling down.)

13/ "They won $500 in 15 minutes at at a $500 maximum table. Then the dealer pressed the secret button.

"An army of unseen operatives inspected the play from behind miles of one-way mirrors. Dealers were expected to inform Smith when someone was winning too much too fast."

14/ "Betting it all only works until you lose.

"The martingale, which requires doubling a wager at every bet lost, can lead to rapidly escalating losses.

"Although it takes a whole to get started, Kelly betting causes wealth to grow fastest by making optimal use of capital."

15/ "Betting twice Kelly ('overbet') is treacherous. Due to a lucky streak, overbettor was briefly the best-performing of the systems early on (the little volcano-shaped peak at lower left). Then the overbettor’s wealth fell back to nearly zero and stayed there for a long time.

16/ "Were the simulation continued indefinitely, the wealth of the twice-Kelly bettor would fall back to the original $1 or less an infinite number of times.

"The Kelly system manages money so that the bettor stays in the game long enough for the law of large numbers to work."

17/ "Card-counting may be the greatest shill ever invented. Not everyone who read Thorp’s book was able to apply the system consistently enough to gain an advantage. For every successful counter, there were hundreds who merely thought they could count cards successfully.

18/ "Card-counting got more attention than the more abstract Kelly formula.

"Those who skimmed Thorp’s book probably did not understand the importance of scaling bets to bankroll. It is a natural impulse to bet big when the deck is hot. For many, this must have been costly."

19/ "Use of multiple decks makes counting less profitable. Because the end cards are never dealt, the concentrations of good cards that occasionally occur at the end of the deck never come into play.

"While playing at one Las Vegas strip casino, Thorp was offered a drink.

20/ "He had problems concentrating and staggered up to his room. His eyes were dilated. It took about eight hours to wear off. The next day, Thorp returned and was offered another drink. He asked for water this time. “It tasted like they’d dumped a box of baking soda in it.

21/ “Just the few drops on my tongue were enough to wipe me out for the night.... I know of three beatings. One well-known blackjack card-counter had a lot of his face caved in. A guy I know had his arms held. Every time he tried to catch his breath, they’d punch him again.”

22/ "The latter player had been told to leave. He ignored the warning and continued playing. Thorp made it a policy to leave when asked on the hopeful theory that the thugs would always give one “fair” warning before getting violent.

23/ "Ed Reid and Ovid Demaris’s The Green Felt Jungle, an exposé of casino corruption, confirms that the casinos settled disputes with gangland violence well into the 1960s. Beatings often took place in the counting room, a soundproof room “ideal for such torture.”

24/ "Reid and Demaris tell of a cheating dealer at the Riviera. Two casino enforcers forced him to place his closed fists on a table. Another used a lead-encased baseball bat to smash the man’s fists. A mob doctor bandaged but did not set the hands.

25/ "The man was driven to the edge of town. The thugs took his shoes off and pushed him out of the car. “Now you SOB,” one thug said, “walk to Barstow. No goddamn hitchhiking, either. We’re gonna check on you all the way.” "

26/ "Bachelier spent his career in such obscurity that virtually nothing is known of his life. He died a decade before his rediscovery by Savage and Samuelson would make him one of the most influential figures in 20th-century economics."

More on this:

https://twitter.com/ReformedTrader/status/1271110594196717569

27/ "At the time Bachelier was writing, Albert Einstein puzzled over Brownian motion. The mathematical treatment of Einstein published in 1905 was similar to but less advanced than the one that Bachelier had already derived for stocks. Einstein had never heard of Bachelier."

28/ "The notion of a superior investor needs to be carefully qualified. The hallmark has to be a market-beating risk-adjusted return achieved not through luck but through some logical system."

AQR evaluates superstar investors using risk-adjusted returns:

https://twitter.com/ReformedTrader/status/1217884016797310976

29/ "Samuelson apparently felt that Buffett’s success was best filed with a small minority of “unexplained cases.” Samuelson, however, hedged his personal bets by putting some of his own money in Berkshire Hathaway."

More on Buffett's alpha:

https://twitter.com/ReformedTrader/status/1128474864770138112

30/ "An MIT “Mafia” made it difficult to publish dissenting views in The Journal of Finance & other prestigious publications. In the 1980s, MIT information theorist Robert Fano wrote a paper arguing that stock price changes are not exactly a random walk & have predictable cycles.

31/ "The reaction to the paper’s mere premise was brutal. He was told that it would be pointless to seek publication. “Unless you have certain views, you’re wrong. The referee would call someone at MIT and they’d say, ‘Oh, yes, he’s a crackpot.’” "

More:

https://twitter.com/ReformedTrader/status/1331998734276653059

32/ "It is folly to bet everything on a favorite (horse or stock). The only way to survive is through diversification.

"There may also be unacknowledged risks. What we believe to be a “sure thing” is not. A small profit may come by accepting a small risk of a catastrophic loss."

33/ "One of the puzzles of the market is that stock prices are more volatile than corporate earnings. This is often attributed to feedback effects.

"When people put money into the market, the buying pressure causes prices to rise. Envy motivates friends into buying stock too.

34/ "Prices can’t go up forever if earnings haven’t increased apace. At some point, bad news triggers panic selling (negative feedback). The “bad news” does not have to be that bad: it's only a catalyst, the pinprick that bursts the bubble."

More on this:

https://twitter.com/ReformedTrader/status/1190258717779849216

35/ "Blackjack had ceased to be as profitable or fun as it had once been for Thorp. “I realized that if I pushed it, some unpleasant physical things would eventually happen in Nevada.” By 1964, he decided to direct his talents toward the biggest casino of all: the stock market."

36/ "Most warrants were cost too much given the odds. This was especially true of warrants within a couple of years of expiring. Traders were too optimistic about the prospect of stock prices rising quickly.

"Should you find a warrant that costs too much, you can sell it short.

37/ "Long-short trades are Kelly-optimal. They were in use in the stock market long before Kelly, though. Thorp’s innovation was to calculate exactly how much of the stock he had to buy to offset the risk of short-selling the warrant. This technique is now called delta hedging."

38/ "Thorp's hedging system worked as he’d hoped. By 1967, he had parlayed his original $40,000 into $100,000.

"There were relatively few warrants out there, so the market was illiquid. Someone who sells short too many warrants may find it difficult to buy them when needed.

39/ "The “artificial” demand created by the deal itself can drive up the prices of these warrants. That is bad because Thorp was betting the warrants would get cheaper.

"Sometimes a company would change the terms of a warrant, and this could be disastrous for the trade.

40/ "For these & other reasons, not every warrant deal turned a profit. Unlike other traders, Thorp understood the concept of gambler’s ruin. He was able to estimate the chances of profit & use the Kelly formula to make sure he was not committing too much money to any one deal."

41/ "Thorp's book seems to have been the first discussion in print of delta hedging. Yet as one of the hundreds of books of advice for the small investor that come out every year, the book received little notice from most academics."

42/ "The meaning of “hedge fund” drifted. Not all hedge funds hedge. Their distinction from mutual funds is now partly socioeconomic.

"Due to voluntary reporting, the public database for hedge funds (TASS) is rife with survivor bias."

More on this:

https://twitter.com/ReformedTrader/status/1233573232881438720

43/ "Thorp and wife met Buffett and wife for a night of bridge at the Buffetts’ home. Thorp was impressed with Buffett’s breadth of interests.

"Ed told Vivian he believed that Buffett would one day be the richest man in America. Buffett’s verdict on Thorp was also positive."

44/ "By 1967, Thorp had devised a version of what are now called the Black-Scholes pricing formulas for options and was thereby able to find mispriced convertible bonds and hedge the deals with the underlying stock."

45/ "The size of Thorp’s investment was limited by the market. The optimal position was “all you can get”—e.g., a mere $2,900 worth of warrants.

"In practice, Thorp could make a quick estimate to confirm that a position was well under the Kelly limit."

46/ "What Milken did with market inefficiencies was entirely different than Thorp did. He was such a superb salesman that, in time, junk bonds came to sell for elevated prices that largely nullified Hickman’s original reason for buying them.

47/ "Companies with doubtful credit issued junk bonds, buy other companies, and sell off their assets to pay the bond interest. When successful, corporate raiding was a form of arbitrage. The acquired companies were sometimes worth more than their irrationally low market values.

48/ "Milken surrounded himself with hardworking loyal people of mediocre talent. He wanted people who would owe everything to him.

"People in Milken’s circle had an almost creepy level of devotion: “Michael is the most important individual who has lived in this century.”

49/ "Yet if his whole life was devoted to making money, he seemed not to care much about spending it. He lived in a relatively unpretentious Encino home, ate lunch off paper plates, wore a reasonably priced toupee, and drove an Oldsmobile.

50/ "Thorp and Regan began using Milken as their fund’s primary broker in the early 1970s. In all the time that Thorp’s fortunes were connected to Milken’s, the two men never met."

More on Milken:

https://twitter.com/ReformedTrader/status/1292156647754747905

51/ "In the early 1970s, Ross and Kimmel believed it might make sense to take Warner Communications private. They wanted to buy back most of the stock issued, limiting ownership to the few biggest shareholders. To get the necessary money, Warner would have to issue junk bonds.

52/ "Milken explained that Ross would have to give up 40% of Warner’s stock as an inducement to get people to buy the junk bonds. This was a standard equity kicker. Drexel would get another 35% cut as payment for services rendered, leaving 25% of the company for Ross’s group.

53/ "Ross had no intention of giving away 75% of the company and dropped the plan.

"Milken repeated this pitch to many clients. What they didn’t know was that the equity kicker was rarely offered to bond buyers. Instead, the stock quietly went into Milken’s private accounts."

54/ "Thorp compared graphs produced by Black and Scholes’s formulas with those from his own. They were the same except for a factor incorporating the risk-free rate. Thorp had not included this because the OTC options he traded did not credit the trader with short-sale proceeds.

55/ " The rules were changed when options began trading on the CBOE. Black and Scholes accounted for this. Otherwise, the formulas were equivalent.

"The Black-Scholes formula, as it was christened, was published in 1973. That name deprived both Merton and Thorp of credit.

56/ "In Merton’s case, it was a matter of courtesy. Because he had built on Black and Scholes’s work, he delayed publishing his derivation until their article appeared.

"Thorp considers the Merton paper “a masterpiece.”

57/ “I never thought about credit... I came from outside the economics and finance profession. The great importance that was attached to this problem wasn’t part of my thinking. What I saw was a way to make a lot of money.”

58/ "There are anomalies challenging every scientific theory ever propounded. It is a tough call knowing which to take seriously.

"EMH generally supposes that it is such a cinch to exploit arbitrage opportunities that prices never get significantly out of line for long.

59/ "Thorp’s experience differed. Arbitrageurs were often constrained by trading costs, the supply of mispriced securities, the Kelly formula, and other factors. It took weeks, months, and more for mispricings to diminish, even with Thorp trying to profit at the maximum rate."

60/ "By Sharpe’s terminology, an active investor need not trade “actively.” A retired teacher with two shares of AT&T counts as an active investor operating on the assumption that AT&T is better to own than a total market index fund.

"Active investing is a zero-sum game."

61/ "Thorp and Regan had turned a conviction that the market can be beaten into one of the most successful investment partnerships of all time, achieving greater-than-market returns over 13 consecutive years."

Thorp in Hedge Fund Market Wizards (thread):

https://twitter.com/ReformedTrader/status/1204621967405408257

62/ "Bet your entire net worth on the flip of a coin. You play against your neighbor, who has the same net worth. It’s double or nothing. Winner gets the loser’s house, car, savings, everything.

"Both of you would be nuts to agree. You have far more to lose than to gain.

63/ "Compute the geometric mean by multiplying the two equally possible outcomes—$200,000 times $0—and taking the square root. Since zero times anything is zero, the geometric mean is zero. Accept that as the true value of the wager, and you’ll stick with your $100,000 net worth.

64/ "The geometric mean is almost always less than the arithmetic mean. (The exception is when all the averaged values are identical. Then the two kinds of mean are the same.) This means that the geometric mean is a more conservative way of valuing risky propositions."

65/ "A wager can make sense when the odds are slanted in one’s favor. It can also make sense when the parties differ in wealth.

"A poor merchant may improve his geometric mean by buying overpriced insurance; the wealthier insurance company is also improving its geometric mean.

66/ "Kelly’s prescription can be restated as this simple rule: When faced with a choice of wagers or investments, choose the one with the highest geometric mean of outcomes. This rule, of broader application than the edge/odds Kelly formula for bet size, is the Kelly criterion."

67/ "The geometric mean, also known as the compound return on investment, is approximately the arithmetic mean minus one-half the variance. This estimate may be made more precise by incorporating further statistical measures."

68/ "The worst wheel, by the Kelly philosophy, is the second. That’s because it has a zero as one of its outcomes. With each spin, you risk losing everything. Any long-term “investor” who lets money ride on the second wheel must eventually go bust: its geometric mean is zero.

69/ "The Kelly criterion would have you put your money on the first wheel (the highest geometric mean, not the highest arithmetic mean).

"A gambler who diversifies by betting on every horse achieves a higher geometric mean than someone who risks everything on a single horse."

70/ "The arithmetic mean return is always higher than the geometric mean. Therefore, a volatile stock with zero geometric mean return must have a positive arithmetic mean return.

"Another good feature of the Kelly criterion is that it maximizes the _median_ wealth.

71/ "What the Kelley system cannot do is engineer luck. It is possible to be unlucky when using the Kelly system, to end up with less than the median. When you do, you may be worse off than you would have been with another system."

72/ "People’s feelings about wealth are fluid, inconsistent, and hard to identify with any neat mathematical function (including logarithmic ones). Preferences are often generated on demand. You do not know what you want until you go to a certain amount of trouble to find out.

73/ "This is hardly news to the organizers of opinion polls and focus groups. People have deep-seated opinions on some issues only. With other issues, you have to press them to decide—and a lot depends on how exactly you phrase the question."

For example,

https://twitter.com/ReformedTrader/status/1454598965639344132

74/ "In stocks, it generally takes years to double your money—or lose practically everything. No buy-and-hold investor lives long enough for a high degree of confidence that the Kelly system will pull ahead of all others. Kelly has more relevance to _traders_ [larger N]."

75/ "Kelly betting is a way of making all gambles and investments interchangeable. Given any gambling or investment opportunity, the Kelly wager converts it into a capital-growth-optimal gamble/investment."

76/ "Betting half Kelly is appealing because it cuts volatility drastically while decreasing the return by only a quarter.

"The full (half) Kelly better stands a 1/3 (1/9) chance of halving her bankroll before she doubles it."

77/ "Bet sizes just to the left of the Kelly bet, and including the Kelly bet itself, are aggressive. Bet sizes to the right of Kelly are insane.

"There is always uncertainty about the true odds, and human nature may further bias estimation error in the direction desired.

78/ "It is easy for the best computer models to overestimate edge by a factor of 2. This means someone attempting to place a Kelly bet might unintentionally at twice Kelly—which cuts the return rate to zero.

"Another method to tame the Kelly system is diversification.

79/ "Pretend you are able to place simultaneous bets on hundreds of identically biased coins. Each coin has a 55% chance of coming up heads and pays even money. As we’ve seen, the Kelly wager for sequential bets on a single such coin is 10% of your bankroll.

80/ "With 100 coins tossed simultaneously, the Kelly wager is nearly 1/100 of the bankroll on each coin. (We don’t stake everything because it’s possible for all hundred coins to come up tails.) Diversification creates smooth exponential growth in which large moves are very rare.

81/ "Diversification works well for team blackjack players because there is no correlation between the luck at one table and the next.

"It worked for Princeton-Newport because the correlations between bets were low; Thorp designed his trades to be market- and volatility-neutral.

82/ "In our global economy, virtually all stocks & stock markets are correlated to varying degrees. A crash in Tokyo depresses stocks in New York.

"Anyone who puts all her assets in stocks must accept large dips in wealth. This has weighed heavily on critics of Kelly investing.

83/ "On October 19, 1987, the Dow lost 23% in a single day. Princeton-Newport’s $600 million portfolio shed only about $2 million in the crash. Thorp’s computer alerted him to rich opportunities in the panicked valuations. There were no buyers, making it impossible to sell.

84/ "Thorp made $2 million profit in new trades that day and the next. Princeton-Newport closed October about even for the month. Most mutual funds were down 20% or more.

"Black Monday was also a severe test of EMH and a clear counterexample to the random-walk model.

85/ "It was difficult to see how a rational market could change 23% in a single day with no major bad news.

"Mark Rubinstein (coinventor of portfolio insurance, which played a role in the crash) estimated the chance of falling 29% (as S&P futures did) in one day as 1/10^160.

86/ Rubinstein: "Such an event that it would not be anticipated to occur even if the stock market were to last for 20 billion years. Indeed, such an event should not occur even if the stock market were to enjoy a rebirth for 20 billion years in each of 20 billion big bangs."

87/ "Over 19 years, Princeton-Newport Partners' compound return averaged 15.1% annually after fees with a SD of 4%. (Buffett’s & Soros’s returns were much more volatile.)

"A chart of Princeton-Newport’s return looks nothing like the the _sequential_ Kelly better’s jittery graph.

88/ "Through diversification, fractional Kelly position sizes, and a philosophy of erring on the side of caution, Thorp achieved a smooth exponential growth refuting the conventional trade-off of risk and return."

89/ "Thorp decided not to put money in LTCM. He was concerned that Merton and Scholes, though brilliant, had little experience. It didn’t help that Merton was second only to Samuelson as a critic of the Kelly criterion. Thorp also had heard that Meriwether was a “martingale man.”

90/ “The general chatter was that he was a high roller, and it wasn’t clear that the size of his bets were justified,” Thorp recalled. “The story was that if he got in the hole, if things went against him, he’d bet more. If things still went against him, he’d bet more.”

91/ "LTCM investors ranged from Merrill Lynch to the Kuwaiti state pension fund; the Bank of China to Hollywood agent Mike Ovitz.

"Some people were so desperate to own a piece of Wall Street’s hottest property that gray-market LTCM shares sold for 10% above asset value.

92/ "After a lukewarm 1997, Meriwether decided to return the money of some of his investors in the hope of boosting future performance. Fortune magazine reported that “many went kicking and screaming, and at least one protested so angrily that LTCM allowed him to stay onboard.”

93/ "LTCM used leverage to multiply small profit opportunities to the point where they were big enough to matter. Paul Samuelson said he had doubts: the fund was placing a lot of faith in the random-walk model. The leverage left little room for any misfit of theory and reality.

94/ "With zero haircuts, LTCM was like a gambler whose pit boss extends him unlimited credit. You might think that with unlimited credit, it’s irrelevant how much money you have. The more you bet, the more you win. Any wager, no matter how high, seems justified.

95/ "This argument might hold water in the case of a casino with literally unlimited credit and bet size. You wouldn’t even need an edge in a casino like that. Martingale would work. In the real world, “unlimited credit” is only a figure of speech.

96/ "A stellar career can end in a few hours. Blown-up traders have failed at the most important judgment: how much money to commit to a trade.

"Should something terrible happen, the money manager pulls out the VaR report and point to cell D18, the 5% risk of a 37% loss.

97/ "Calculating VaR is a practical idea in a litigious society where well-off people don’t know much math.

"VaR reports give the impression that the numbers are reliable because smart people have worked them out, but numbers are only as good as the assumptions underlying them.

98/ "VaR sidesteps the two central questions in John Kelly’s analysis: What level of risk will lead to the highest long-run return? What is the chance of losing everything? (A VaR report could address the second. In practice, it rarely does. Who wants to freak the client out?)

99/ "In July 1998, the IMF made a $17 billion loan package to Russian banks. $4.5 billion of it was wired to mobsters’ offshore bank accounts. The thug-controlled banks had no intention of repaying many of the Western loans. The Russian treasury was scarcely more credit-worthy.

100/ "Russia’s treasury bonds, called GKOs, were the junkiest of junk bonds, paying 40%+ interest. Half of Russia’s tax collections went to pay interest on treasury debt.

"Prime Minister Sergei Kiriyenko announced that Russia was devaluing the ruble and defaulting on the GKOs.

101/ "LTCM instantly lost millions. It was lucky; others did worse.

"Everyone shifted funds from riskier investments to safer, more liquid ones.

"LTCM’s philosophy was that people pay too much for safe, liquid investments. The Russian default temporarily changed that.

102/ "LTCM shed $551 million. It desperately needed collateral to cover its simultaneous losing trades.

“When you’re down by half, people figure you can go down all the way. They’re going to push the market against you. They’re not going to roll your trades. You’re finished.”

103/ Mark Twain: “A banker lends you his umbrella when the sun is shining but wants it back the moment it rains.”

“They should have pulled down their leverage multiple. Instead, they allowed it to drift up to 60x. No Las Vegas gambler would make that mistake - no surviving one.”

104/ "LTCM was simultaneously making nearly the same bets all over the world. This was supposed to be diversification, but it wasn’t. The Russian default affected credit all over the world.

"The banks would soon rush to seize such collateral & sell it, causing prices to plunge.

105/ “I’m not worried about markets trading down. I’m worried they won’t trade at all.”

"Many of the partners had rolled substantial fortunes into LTCM. Hilibrand had taken out a personal loan of $24 million to buy his own fund, which was itself at nosebleed leverage levels.

106/ "Hilibrand’s net worth went from $100 million to $20 million in debt. He requested that the bailout cover his personal debts. The consortium said no. Buffett marveled at how “ten or 15 guys with an IQ of 170” could get themselves “into a position to lose all their money.”

107/ "LTCM had based some models only four years of data. In that short period, the spread between junk bonds and treasuries hovered in the range of 3-4 percentage points. The fund essentially bet that it would not exceed this range. But as recently as 1990, it had topped 9%.

108/ Thorp: “People think that things are necessarily bounded in a historical range.” In 1998, when the spread widened suddenly to 6%, “they said this was a one-in-a-million-year event. A year or two later, it got wider, and two years after that, it got wider yet.”

109/ "Overbetting (unlike leverage or fat tails) is always bad. Thorp linked the LTCM collapse to Merton and Scholes’s intellectual critique of the Kelly system.

"Too little of the fund’s brainpower went to asking what could have gone wrong.

110/ "When financial models can be so incredibly wrong, the extreme downside caution of Kelly betting is not out of place. For mathematical, psychological, and sociological reasons, it is a good idea to use a money management system that is forgiving of estimation errors.

111/ "The University of British Columbia’s William Ziemba has estimated that LTCM’s leverage was somewhere around twice the Kelly level. If correct, that would imply that the fund’s true compound growth rate was hovering near zero."

More on LTCM:

https://twitter.com/ReformedTrader/status/1271108014498385920

112/ "The manager shares the upside but does not directly share the investors’ losses.

"Investors choose one fund over another on the strength of a few basis points of return. This creates the severest temptation for managers to boost return any way possible.

113/ "One way is to take “Russian roulette” risks likely to pay off in the short run but carry the possibility of disaster. Human nature and single-period financial models make it easy to blind oneself to long-term risk. It can take years for overbetting to blow up.

114/ "There is no better way of demonstrating the need for money management than seeing your own money vanish while making positive-expectation bets. It is impossible to make the same point so viscerally with mere stochastic differential equations."

115/ "Thorp continued to tinker with statistical arbitrage. He replaced the division by industry groups with a more flexible factor analysis system that analyzed stocks by correlations with factors such as market indexes, inflation, and gold. This better managed risks.

116/ "Because of their unpredictability, mergers, spin-offs, and reorganizations were bad for the scheme. At the announcement of such news, Mizusawa put the affected companies on a “restricted list” of stocks to avoid in new trades.

117/ "The inexplicable aspect of Thorp’s achievement was his continuing ability to discover new market inefficiencies as old ones played out.

"In May 1998, Thorp reported that his investments had grown at an average 20% annual return (with 6% SD) over 28.5 years."

118/ "Ziemba estimates that a first-rate Hong Kong computer team can make $100 million in a good season. Races are an instructive model of securities markets. The same fallible humans set prices for tech stocks & show bets. The profit motive does not guarantee market efficiency.

119/ "Hakansson estimates that no more than 10% of MBA programs mention the Kelly criterion.

Jarrod Wilcox: “You’ve heard of Kuhn’s paradigm shift? This is what’s going on. Until you get leading lights at MIT or Stanford to endorse it, you’re not going to have a paradigm shift.

120/ “At one point, I was so daring as to submit a paper to The Journal of Finance. The review said, ‘This contradicts everything we’ve learned in finance.’

“It really doesn’t. But it contradicts so many things that the claws come out.”

More on Kuhn:

https://twitter.com/ReformedTrader/status/1331998734276653059

121/ "There's a BIG difference between *arithmetic* (serial) and *geometric* (compounded) expectations.

"The *arithmetic* expectation of a '50/50 doubling or halving' bet is +25%.

"The *geometric* expectation of the SAME bet is ZERO."

https://twitter.com/10kdiver/status/1451999570443964417

122/ Related reading:

Red-Blooded Risk: The Secret History of Wall Street

https://twitter.com/ReformedTrader/status/1365779414873608195

Hedge Fund Market Wizards

https://twitter.com/ReformedTrader/status/1202766501956087808

More Money Than God: Hedge Funds and the Making of a New Elite

https://twitter.com/ReformedTrader/status/1320532729541267457

Leveraged Trading

https://twitter.com/ReformedTrader/status/1229120228425994246